His argument is in Euclidean quantum gravity, which he describes as "the only sane way to do quantum gravity non-perturbatively", something which some might disagree with. What he seems to be arguing is that, while it is true you get information loss in the path integral over metrics on a fixed non-trivial black hole topology, you really need to sum over all topologies. When you do this you get unitary evolution from the trivial (no black hole) topology and the non-trivial topologies give contributions that are independent of the initial state and don't contribute to the initial-final state amplitude.

I guess what this means is that he is claiming that, sure, if you knew you really had a black hole, then there would be a problem with unitarity, but in quantum gravity you don't ever really know that you have a black hole, you also have to take into account the amplitude for not actually having one and when you properly do this the unitarity problem goes away.
...
---quote---

trivial topology means no black hole

some kind of shell game? My impression is that to find if information is lost in a black hole in ordinary QG one would condition on having a black hole
the probabilities would be conditional probabilities given that you have a black hole

But he says "in quantum gravity (at least in his kind) you cant assume you have a black hole" so you average things up including the cases where you dont have a black hole and presto! information is not lost!

in the cases where you do have a black hole (the nontrivial topology)
then he says information IS lost, after all, but in (his special kind of) path integral those cases do not contribute anything to the average because they zero out

so he has a special kind of path integral formalism that zeros out the existence of black holes---does not register the existence of black holes when you do add up the path integral

with this formalism he discovers things about black holes which he wants to tell us----the information in them does not die by the time the hole evaporates, he says

but why should it not? what reasoning has he given that it doesnt?

There was not proposed a mechanism for the info to get out: there was only offered an argument that logically it MUST somehow get out before the hole evaporates.

Hawking argument does not, as far as I can see, offer any resistance to the claim of Gambini Porto Pullin that info fallen into hole will die naturally by time hole evaporates.

I'm hoping other PF folk had other reactions to Hawking's talk and will post them. Would like to see how others reacted.

Brad, thanks so much for replying! I am looking for some PF person who feels they understand the basic argument and who is NOT suspicious.

You and I can remain politely skeptical---but where is someone who will
raise Hawking's banner and explain to us why we ought to believe his path integral?

the argument depends heavily on the Hawking path integral, on its zeroing-out the spacetimes that have black holes living in them and only including one's that dont in the average. This hawking path integral AFAIK has been around since the 1980s and has been worked on sporadically but has gained few adherents as an approach to QG.

what can waiting around for his more detailed paper do for us, if the paper just grinds thru a bunch of Hawking-style path integral calculation that, in any case, does not currently seem of great interest as an approach to gravity?

's gotta be more.

maybe the subsequent paper will stir up greater interest in Euclidean Path Integral.

Well, his paper will hopefully more fully explain his reasoning. The Hawking path-integrals seem to be a bit of a slight of hand right now to me. As it stands right now, until I see his full paper with the mathematics and reasoning, I'm forced to reach the conclusion that while his approach may well show it is unitary, it isn't fundamental. Sort of like renormalization, those infinities really shouldn't be there in the first place. That is what this strikes me as. Yeah, we can cancel out those spacetimes with black holes, but his arguement rests on the fact we can only infer a black hole at distance infinity. Apparently, attempting to measure the field value at some distance between is impossible due to quantum uncertainty. What pray tell, are we to conclude then if we happen to be very close to a black hole?

...And then there's Jaques Distler , who says the information problem was solved years ago in AdS/CFT. everybody knows this he says, but some of the obvious things about Ads/CFT that he talks about were unknown to me.

Hey Jeff! You're a holography maven aren't you? Could you give us a little rundown on this stuff?

"Black hole formation and evaporation, can be thought of as a
scattering process. One sends in particles and radiation from
infinity, and measures what comes back out to infinity. All
measurements are made at infinity, where fields are weak, and one
never probes the strong field region in the middle. So one can't be
sure a black hole forms, no matter how certain it might be in
classical theory. I shall show that this possibility, allows
information to be preserved, and to be returned to infinity."

I take infinity to mean "far field" eg; "no near field effects".
I'm gonna have to think about how information can be returned if the hole is never formed.
Thanks marcus .... reread your post ... now i get it. it averages to get some information back.

Distler is right of course. Sure, its perfectly sensible from a working poitn of view, to impose a negative cc to regularize the path integral since you can benefit from the ads/cft correspondance, but the problem is not solved until you can generalize it to flat or Desitter space. Otoh, its nice to have a working theory that explains things on the bulk. A full fledged Ads/Cft that goes both ways and is known precisely is always of interest. (which will have to wait and see until the full paper is out)

The actual physical path integral itself otoh is not well defined, as you are abusing wick's theorem if you insist on analytically continuing over *all* metrics. It boils down to an operator ordering problem, and an issue with how to define time.

There are other problems I think, but its probably best to reserve judgement until the final paper is released.

Well, he claims to have shown that the nontrivial topologies are removable in the euclidean path integral, in that they are able to be divided out, hence the thing is unitary since the trivial ones are unitary.

But, as per usual, we are not interested in the Euclidean path integral, but rather the lorentzian one, and it isn't clear how to retrieve that mathematically. But whatever, even if that is the case, there is still problems with the picture.